Introduction to Mechanistic/Simulation Modeling

Slides: https://www.andreashandel.com/presentations/

2025-05-29

Modeling definition

The term modeling usually means (in science) the description and analysis of a system using mathematical or computational models.
Many different types of modeling approaches exist. Simulation/mechanistic models are one type (with many subtypes).

Phenomenological/non-mechanistic/heuristic/(statistical) models
- Look at patterns in data
- Do not describe mechanisms leading to the data
Mechanistic/process/simulation models
- Try to represent simplified versions of mechanisms
- Can be used with and without data

You are likely familiar with statistical models (that includes Machine Learning, AI, Deep Learning,…).
Most of those models are phenomenological/non-mechanistic (and static).
Those models are used extensively in all areas of science.
The main goal of these models is to understand data/patterns and make predictions.

Wu et al 2019 Nature Communications.

Finding correlations/patterns is (relatively) simple.
Some models are very good at predicting (e.g. Netflix, Google Translate).
Sometimes we can go from correlation to causation.
We don’t need to understand all the underlying mechanisms to get actionable insights.

The jump from correlation to causation is always tricky (bias/confounding/systematic errors).
Even if we can assume a causal relation, we do not gain a lot of mechanistic insights or deep understanding of the system.

We formulate explicit mechanisms/processes driving the system dynamics.
This is done using mathematical equations (often ordinary differential equations), or computer rules.
Also called systems/dynamic(al)/ (micro)simulation/process/ mathematical/ODE/… models.

We need to know (or assume) something about the mechanisms driving our system to build a mechanistic model.
If our assumptions/model are wrong, the “insights” we gain from the model are spurious.

Non-mechanistic models (e.g. regression models, machine learning) are useful to see if we can find patterns in our data and possibly predict, without necessarily trying to understand the mechanisms.
Mechanistic models are useful if we want to study the mechanism(s) by which observed patterns arise.

Ideally, you want to have both in your ‘toolbox’.

www.gocomics.com/nonsequitur

Using a TB model to explore/predict cytokine-based interventions (Wigginton and Kirschner, 2001 J Imm).

\[ \begin{aligned} \dot V & = rV-kVT^*\\ \dot P & = fV - dP \\ \dot T & = -aPT \\ \dot T^* & = aPT + gT^* \end{aligned} \]

Targeted antiviral prophylaxis against an influenza pandemic (Germann et al 2006 PNAS).

Within-host/individual level	Between-host/population level
Spread inside a host (virology, microbiology, immunology)	Spread on the population level (ecology, epidemiology)
Populations of pathogens & immune response components	Populations of hosts (humans, animals)
Acute/Persistent (e.g. Flu/TB)	Epidemic/Endemic (e.g. Flu/TB)
Usually (but not always) explicit modeling of pathogen	Often, but not always, no explicit modeling of pathogen

The same types of simulation models are often used on both scales.

\[ \begin{aligned} \dot{B} & = g B(1-\frac{B}{B_{max}}) - d_B B - kBI\\ \dot{I} & = r BI - d_I I \end{aligned} \]

\[ \begin{aligned} \dot{B} & = g B(1-\frac{B}{B_{max}}) - d_B B - kBI\\ \dot{I} & = r BI - d_I I \end{aligned} \]

The left side is the change in time of the indicated variable.
Each term on the right side represents a (often simplified/abstracted) biological process/mechanism.
Any positive term on the right side is an inflow and leads to an increase of the indicated variable.
Any negative term on the right side is an outflow and leads to a decrease of the indicated variable.

It is important to go back and forth between words, diagrams, equations.
Diagrams specify a model somewhat, but not completely. The diagram below could be implemented as ODEs or discrete time or stochastic models.

We could analyze the model behavior with ‘pencil and paper’ (or some software, e.g. Mathematica/Maxima). This only works for simple models.
We could analyze the model behavior by simulating it.
To simulate, we need to implement the model on a computer, specify starting (initial) conditions for all variables and values for all model parameters.